A bit more about WAAS and Differential GPS....
The ground reference station is located at a very accurately known location (surveyed), say on an airport for sake of argument. This reference station also receives the same GPS signal as is received in the cockpit by the GPS. The ground reference station then compares the position derived from the raw GPS with its known location and calculates any error, then re-broadcasts this error (via RF, satellite, Spot beam etc....) so that the GPS in the cockpit can "correct" its position by applying the same error correction. This can actually achieve millimetric accuracy if the GRS is relatively close to the GPS it is correcting.
You probably won't have a reference station right in your vicinity so when using differential GPS then a number of GRSs are normally used which may be located hundreds of miles apart and the results of all of them are averaged to give an overall correction to apply to the GPS. This was particularly useful in the old days when the US military used top apply selective availability to the GPS signal to deliberately introduce errors to keep accuracy above say 100m. Using reference stations one could pretty much "undo" a these errors to give 5m or so accuracy. Back in 2000 the errors were turned off and Clinton signed a memorandum stating that the US would not turn off or scramble GPS signals again.
Rather than invest in their own system, I think Europe should have offered to invest in GPS and possibly shared some of the control over it, and maybe even have a second control centre in somewhere like Geneva, which would ensure its integrity, rather than re-inventing the wheel which is what seems to be the Euro way....GPS is a standard, and is always going to be better than any new system, so why not just help improve it rather than waste billions on a new project.